Question: Solve for $x$ and $y$ using elimination. ${-4x+6y = 32}$ ${-3x-5y = -33}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $-4$ ${-12x+18y = 96}$ $12x+20y = 132$ Add the top and bottom equations together. $38y = 228$ $\dfrac{38y}{{38}} = \dfrac{228}{{38}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-4x+6y = 32}\thinspace$ to find $x$ ${-4x + 6}{(6)}{= 32}$ $-4x+36 = 32$ $-4x+36{-36} = 32{-36}$ $-4x = -4$ $\dfrac{-4x}{{-4}} = \dfrac{-4}{{-4}}$ ${x = 1}$ You can also plug ${y = 6}$ into $\thinspace {-3x-5y = -33}\thinspace$ and get the same answer for $x$ : ${-3x - 5}{(6)}{= -33}$ ${x = 1}$